Question

How many different ways are there to arrange the 6 letters in the word SUNDAY?

Answer 1

There are 720 different ways to arrange the 6 letters in SUNDAY.

Explanation:

The first letter of the rearrangement can be any 1 of 6 letters.

The second letter can now be any 1 of 5 letters. So the first two letters can be a combination of `color(red)(6 xx 5)` letters or `color(red)(30)` arrangements.

The third letter can be any 1 of 4 remaining letters. So the first three letters can be a combination of `color(red)(6 xx 5 xx 4)` letters or `color(red)(120)` arrangements.

The fourth letter can now be any 1 of 3 remaining letters. So the first four letters can be a combination of `color(red)(6 xx 5 xx 4 xx 3)` letters or `color(red)(360)` arrangements.

The fifth letter can now be only 1 of 2 remaining letters. So the first five letters can be a combination of `color(red)(6 xx 5 xx 4 xx 3 xx 2)` letters or `color(red)(720)` arrangements.

The final letter can now be only 1 letter because all of the others have been used. So the six letters can be a combination of `color(red)(6 xx 5 xx 4 xx 3 xx 2 xx 1)` letters or `color(red)(720)` arrangements.